"Helms have a common enough purpose: to protect the vulnerable, fleshy parts of the head from skull cracks, and make gouging eyes out a bit harder. Sturdier helms can weigh quite a bit in exchange for providing ample protection."— Game Guide(src)
Unlike Diablo I, helms are actually shown on a character model in Diablo II, but Circlets are a way to give heroes a bare-headed look.
In Diablo III, helms offer a major bulk of Armor, and in addition to all-item affixes, may roll resistances, one Socket, Critical Hit chance, increased damage of secondary skills, Life %, Life regeneration, Life per Hit, Thorns, health globe / gold pickup range, status effect duration reduction, experience, and chance to Fear on hit. Legendary helms often roll other stats.
In Diablo III, helms are a visible piece of equipment, and may be transmogrified or just made 'disappear' with the use of Vanishing Dye. Any helm may be transmogrified into a class-specific helm (Wizard Hat, Voodoo Mask or Spirit Stone), but only by the respective class characters. Class-specific helms may be transmogrified into normal helms without restrictions.Some helms, when equipped, alter the character's hairstyle, hiding excessive hair from view.